You could just assign the hit points that fit, and the CON that fits, and cut out the mediating term!I think it's fair to call hit dice the glue that binds hit points and Constitution.
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suppose one is designing a creature and has both a sense of how tough it should be in the abstract game-driven sense (hp) and how tough it should be in a more fiction-driven sense (Constitution). Hit dice adds a degree of freedom which allows one to hit both targets in the same mechanical framework.
Because of that, I think the other reasons you give for including hit dice are more compelling.